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fe_engine_template.hh
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/**
* Copyright (©) 2010-2023 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* This file is part of Akantu
*
* Akantu is free software: you can redistribute it and/or modify it under the
* terms of the GNU Lesser General Public License as published by the Free
* Software Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* Akantu is distributed in the hope that it will be useful, but WITHOUT ANY
* WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
* A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
*/
/* -------------------------------------------------------------------------- */
#include "fe_engine.hh"
/* -------------------------------------------------------------------------- */
#include <type_traits>
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
#ifndef AKANTU_FE_ENGINE_TEMPLATE_HH_
#define AKANTU_FE_ENGINE_TEMPLATE_HH_
namespace akantu {
class Integrator;
class ShapeFunctions;
} // namespace akantu
namespace akantu {
class DOFManager;
namespace fe_engine {
namespace details {
template <ElementKind> struct AssembleLumpedTemplateHelper;
template <ElementKind> struct AssembleFieldMatrixHelper;
} // namespace details
} // namespace fe_engine
template <ElementKind, typename> struct AssembleFieldMatrixStructHelper;
struct DefaultIntegrationOrderFunctor {
template <ElementType type> static inline constexpr int getOrder() {
return ElementClassProperty<type>::polynomial_degree;
}
};
/* -------------------------------------------------------------------------- */
template <template <ElementKind, class> class I, template <ElementKind> class S,
ElementKind kind = _ek_regular,
class IntegrationOrderFunctor = DefaultIntegrationOrderFunctor>
class FEEngineTemplate : public FEEngine {
/* ------------------------------------------------------------------------ */
/* Constructors/Destructors */
/* ------------------------------------------------------------------------ */
public:
using Integ = I<kind, IntegrationOrderFunctor>;
using Shape = S<kind>;
FEEngineTemplate(Mesh & mesh, Int spatial_dimension = _all_dimensions,
const ID & id = "fem", bool do_not_precompute = false);
~FEEngineTemplate() override;
/* ------------------------------------------------------------------------ */
/* Methods */
/* ------------------------------------------------------------------------ */
public:
/// pre-compute all the shape functions, their derivatives and the jacobians
void initShapeFunctions(GhostType ghost_type = _not_ghost) override;
void initShapeFunctions(const Array<Real> & nodes,
GhostType ghost_type = _not_ghost);
/* ------------------------------------------------------------------------ */
/* Integration method bridges */
/* ------------------------------------------------------------------------ */
/// integrate f for all elements of type "type"
void
integrate(const Array<Real> & f, Array<Real> & intf, Int nb_degree_of_freedom,
ElementType type, GhostType ghost_type = _not_ghost,
const Array<Idx> & filter_elements = empty_filter) const override;
/// integrate a scalar value on all elements of type "type"
[[nodiscard]] Real
integrate(const Array<Real> & f, ElementType type,
GhostType ghost_type = _not_ghost,
const Array<Idx> & filter_elements = empty_filter) const override;
/// integrate one element scalar value on all elements of type "type"
[[nodiscard]] Real
integrate(const Ref<const VectorXr> f, ElementType type, Int index,
GhostType ghost_type = _not_ghost) const override;
private:
template <ElementKind kind_ = kind, typename D1, typename D2, typename D3,
std::enable_if_t<aka::are_vectors<D1, D3>::value and
kind_ == _ek_regular> * = nullptr>
inline void interpolateImpl(const Eigen::MatrixBase<D1> & real_coords,
const Eigen::MatrixBase<D2> & nodal_values,
Eigen::MatrixBase<D3> & interpolated,
const Element & element) const;
template <ElementKind kind_ = kind, typename D1, typename D2, typename D3,
std::enable_if_t<aka::are_vectors<D1, D3>::value and
kind_ != _ek_regular> * = nullptr>
inline void interpolateImpl(const Eigen::MatrixBase<D1> & /*real_coords*/,
const Eigen::MatrixBase<D2> & /*nodal_values*/,
Eigen::MatrixBase<D3> & /*interpolated*/,
const Element & /*element*/) const {
AKANTU_TO_IMPLEMENT();
}
public:
/// interpolate on a phyiscal point inside an element
void interpolate(const Ref<const VectorXr> real_coords,
const Ref<const MatrixXr> nodal_values,
Ref<VectorXr> interpolated,
const Element & element) const override;
/// get the number of integration points
[[nodiscard]] Int
getNbIntegrationPoints(ElementType type,
GhostType ghost_type = _not_ghost) const override;
/// get shapes precomputed
[[nodiscard]] const Array<Real> & getShapes(ElementType type,
GhostType ghost_type = _not_ghost,
Int id = 0) const override;
/// get the derivatives of shapes
[[nodiscard]] const Array<Real> &
getShapesDerivatives(ElementType type, GhostType ghost_type = _not_ghost,
Int id = 0) const override;
/// get integration points
[[nodiscard]] inline const Matrix<Real> &
getIntegrationPoints(ElementType type,
GhostType ghost_type = _not_ghost) const override;
/* ------------------------------------------------------------------------ */
/* Shape method bridges */
/* ------------------------------------------------------------------------ */
/// compute the gradient of a nodal field on the integration points
void gradientOnIntegrationPoints(
const Array<Real> & u, Array<Real> & nablauq, Int nb_degree_of_freedom,
ElementType type, GhostType ghost_type = _not_ghost,
const Array<Idx> & filter_elements = empty_filter) const override;
/// interpolate a nodal field on the integration points
void interpolateOnIntegrationPoints(
const Array<Real> & u, Array<Real> & uq, Int nb_degree_of_freedom,
ElementType type, GhostType ghost_type = _not_ghost,
const Array<Idx> & filter_elements = empty_filter) const override;
/// interpolate a nodal field on the integration points given a
/// by_element_type
void interpolateOnIntegrationPoints(
const Array<Real> & u, ElementTypeMapArray<Real> & uq,
const ElementTypeMapArray<Idx> * filter_elements =
nullptr) const override;
/// pre multiplies a tensor by the shapes derivaties
void
computeBtD(const Array<Real> & Ds, Array<Real> & BtDs, ElementType type,
GhostType ghost_type,
const Array<Idx> & filter_elements = empty_filter) const override;
/// left and right multiplies a tensor by the shapes derivaties
void
computeBtDB(const Array<Real> & Ds, Array<Real> & BtDBs, Int order_d,
ElementType type, GhostType ghost_type,
const Array<Idx> & filter_elements = empty_filter) const override;
/// left multiples a vector by the shape functions
void computeNtb(const Array<Real> & bs, Array<Real> & Ntbs, ElementType type,
GhostType ghost_type,
const Array<Idx> & filter_elements) const override;
/// left and right multiplies a tensor by the shapes
void
computeNtbN(const Array<Real> & bs, Array<Real> & NtbNs, ElementType type,
GhostType ghost_type,
const Array<Idx> & filter_elements = empty_filter) const override;
/// compute the position of integration points given by an element_type_map
/// from nodes position
inline void computeIntegrationPointsCoordinates(
ElementTypeMapArray<Real> & quadrature_points_coordinates,
const ElementTypeMapArray<Idx> * filter_elements =
nullptr) const override;
/// compute the position of integration points from nodes position
inline void computeIntegrationPointsCoordinates(
Array<Real> & quadrature_points_coordinates, ElementType type,
GhostType ghost_type = _not_ghost,
const Array<Idx> & filter_elements = empty_filter) const override;
/// interpolate field at given position (interpolation_points) from given
/// values of this field at integration points (field)
inline void interpolateElementalFieldFromIntegrationPoints(
const ElementTypeMapArray<Real> & field,
const ElementTypeMapArray<Real> & interpolation_points_coordinates,
ElementTypeMapArray<Real> & result, GhostType ghost_type,
const ElementTypeMapArray<Idx> * element_filter) const override;
/// Interpolate field at given position from given values of this field at
/// integration points (field)
/// using matrices precomputed with
/// initElementalFieldInterplationFromIntegrationPoints
inline void interpolateElementalFieldFromIntegrationPoints(
const ElementTypeMapArray<Real> & field,
const ElementTypeMapArray<Real> &
interpolation_points_coordinates_matrices,
const ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
ElementTypeMapArray<Real> & result, GhostType ghost_type,
const ElementTypeMapArray<Idx> * element_filter) const override;
/// Build pre-computed matrices for interpolation of field form integration
/// points at other given positions (interpolation_points)
inline void initElementalFieldInterpolationFromIntegrationPoints(
const ElementTypeMapArray<Real> & interpolation_points_coordinates,
ElementTypeMapArray<Real> & interpolation_points_coordinates_matrices,
ElementTypeMapArray<Real> & quad_points_coordinates_inv_matrices,
const ElementTypeMapArray<Idx> * element_filter = nullptr) const override;
/// find natural coords from real coords provided an element
void inverseMap(const Ref<const VectorXr> real_coords, Int element,
ElementType type, Ref<VectorXr> natural_coords,
GhostType ghost_type = _not_ghost) const;
/// return true if the coordinates provided are inside the element, false
/// otherwise
inline bool contains(const Ref<const VectorXr> real_coords, Int element,
ElementType type,
GhostType ghost_type = _not_ghost) const;
private:
template <ElementKind kind_ = kind, typename D1, typename D2,
std::enable_if_t<aka::are_vectors<D1, D2>::value and
kind_ != _ek_cohesive> * = nullptr>
inline void computeShapesImpl(const Eigen::MatrixBase<D1> & real_coords,
Int element, ElementType type,
Eigen::MatrixBase<D2> & shapes,
GhostType ghost_type = _not_ghost) const;
template <ElementKind kind_ = kind, typename D1, typename D2,
std::enable_if_t<aka::are_vectors<D1, D2>::value and
kind_ == _ek_cohesive> * = nullptr>
inline void computeShapesImpl(const Eigen::MatrixBase<D1> & /*real_coords*/,
Int /*element*/, ElementType /*type*/,
Eigen::MatrixBase<D2> & /*shapes*/,
GhostType /*ghost_type*/ = _not_ghost) const {
AKANTU_TO_IMPLEMENT();
}
template <ElementKind kind_ = kind, typename D1, typename D2,
std::enable_if_t<aka::is_vector_v<D1> and kind_ != _ek_cohesive> * =
nullptr>
inline void
computeShapeDerivativesImpl(const Eigen::MatrixBase<D1> & real_coords,
Int element, ElementType type,
Eigen::MatrixBase<D2> & shape_derivatives,
GhostType ghost_type = _not_ghost) const;
template <ElementKind kind_ = kind, typename D1, typename D2,
std::enable_if_t<aka::is_vector_v<D1> and kind_ == _ek_cohesive> * =
nullptr>
inline void
computeShapeDerivativesImpl(const Eigen::MatrixBase<D1> & /*real_coords*/,
Int /*element*/, ElementType /*type*/,
Eigen::MatrixBase<D2> & /*shape_derivatives*/,
GhostType /*ghost_type*/ = _not_ghost) const {
AKANTU_TO_IMPLEMENT();
}
public:
/// compute the shape on a provided point
inline void computeShapes(const Ref<const VectorXr> real_coords, Int element,
ElementType type, Ref<VectorXr> shapes,
GhostType ghost_type = _not_ghost) const override {
this->template computeShapesImpl(real_coords, element, type, shapes,
ghost_type);
}
/// compute the shape derivatives on a provided point
inline void
computeShapeDerivatives(const Ref<const VectorXr> real_coords, Int element,
ElementType type, Ref<MatrixXr> shape_derivatives,
GhostType ghost_type = _not_ghost) const override {
this->template computeShapeDerivativesImpl<kind>(
real_coords, element, type, shape_derivatives, ghost_type);
}
/* ------------------------------------------------------------------------ */
/* Other methods */
/* ------------------------------------------------------------------------ */
/// pre-compute normals on integration points
void
computeNormalsOnIntegrationPoints(GhostType ghost_type = _not_ghost) override;
void
computeNormalsOnIntegrationPoints(const Array<Real> & field,
GhostType ghost_type = _not_ghost) override;
void computeNormalsOnIntegrationPoints(
const Array<Real> & field, Array<Real> & normal, ElementType type,
GhostType ghost_type = _not_ghost) const override;
template <ElementType type, ElementKind kind_ = kind,
std::enable_if_t<kind_ != _ek_regular> * = nullptr>
void computeNormalsOnIntegrationPoints(const Array<Real> & /*field*/,
Array<Real> & /*normal*/,
GhostType /*ghost_type*/) const {
AKANTU_TO_IMPLEMENT();
}
template <
ElementType type, ElementKind kind_ = kind,
std::enable_if_t<kind_ == _ek_regular and type != _point_1> * = nullptr>
void computeNormalsOnIntegrationPoints(const Array<Real> & field,
Array<Real> & normal,
GhostType ghost_type) const;
template <
ElementType type, ElementKind kind_ = kind,
std::enable_if_t<kind_ == _ek_regular and type == _point_1> * = nullptr>
void computeNormalsOnIntegrationPoints(const Array<Real> & field,
Array<Real> & normal,
GhostType ghost_type) const;
public:
/// function to print the contain of the class
void printself(std::ostream & stream, int indent = 0) const override;
void assembleFieldLumped(
const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
ElementType type, GhostType ghost_type) const override;
private:
template <ElementKind kind_ = kind,
std::enable_if_t<kind_ != _ek_cohesive> * = nullptr>
void assembleFieldMatrixImpl(
const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
ElementType type, GhostType ghost_type) const;
template <ElementKind kind_ = kind,
std::enable_if_t<kind_ == _ek_cohesive> * = nullptr>
void assembleFieldMatrixImpl(
const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
ElementType type, GhostType ghost_type) const;
public:
/// assemble a field as a matrix (ex. rho to mass matrix)
void assembleFieldMatrix(
const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
ElementType type, GhostType ghost_type) const override {
this->assembleFieldMatrixImpl(field_funct, matrix_id, dof_id, dof_manager,
type, ghost_type);
}
private:
friend struct fe_engine::details::AssembleLumpedTemplateHelper<kind>;
friend struct fe_engine::details::AssembleFieldMatrixHelper<kind>;
friend struct AssembleFieldMatrixStructHelper<kind, void>;
/// templated function to compute the scaling to assemble a lumped matrix
template <ElementType type>
void assembleFieldLumped(
const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
GhostType ghost_type) const;
/// @f$ \tilde{M}_{i} = \sum_j M_{ij} = \sum_j \int \rho \varphi_i \varphi_j
/// dV = \int \rho \varphi_i dV @f$
template <ElementType type>
void assembleLumpedRowSum(const Array<Real> & field, const ID & matrix_id,
const ID & dof_id, DOFManager & dof_manager,
GhostType ghost_type) const;
/// @f$ \tilde{M}_{i} = c * M_{ii} = \int_{V_e} \rho dV @f$
template <ElementType type>
void assembleLumpedDiagonalScaling(const Array<Real> & field,
const ID & matrix_id, const ID & dof_id,
DOFManager & dof_manager,
GhostType ghost_type) const;
/// assemble a field as a matrix (ex. rho to mass matrix)
template <ElementType type>
void assembleFieldMatrix(
const std::function<void(Matrix<Real> &, const Element &)> & field_funct,
const ID & matrix_id, const ID & dof_id, DOFManager & dof_manager,
GhostType ghost_type) const;
#ifdef AKANTU_STRUCTURAL_MECHANICS
/// assemble a field as a matrix for structural elements (ex. rho to mass
/// matrix)
template <ElementType type>
void assembleFieldMatrix(const Array<Real> & field_1,
Int nb_degree_of_freedom, SparseMatrix & M,
Array<Real> * n,
ElementTypeMapArray<Real> & rotation_mat,
GhostType ghost_type) const;
#endif
/* ------------------------------------------------------------------------ */
/* Mesh Event Handler interface */
/* ------------------------------------------------------------------------ */
public:
void onElementsAdded(const Array<Element> & /*new_elements*/,
const NewElementsEvent & /*unused*/) override;
void onElementsRemoved(const Array<Element> & /*unused*/,
const ElementTypeMapArray<Idx> & /*unused*/,
const RemovedElementsEvent & /*unused*/) override;
void onElementsChanged(const Array<Element> & /*unused*/,
const Array<Element> & /*unused*/,
const ElementTypeMapArray<Idx> & /*unused*/,
const ChangedElementsEvent & /*unused*/) override;
/* ------------------------------------------------------------------------ */
/* Accessors */
/* ------------------------------------------------------------------------ */
public:
/// get the shape class (probably useless: see getShapeFunction)
const ShapeFunctions & getShapeFunctionsInterface() const override {
return shape_functions;
};
/// get the shape class
const Shape & getShapeFunctions() const { return shape_functions; };
/// get the integrator class (probably useless: see getIntegrator)
const Integrator & getIntegratorInterface() const override {
return integrator;
};
/// get the integrator class
const Integ & getIntegrator() const { return integrator; };
/* ------------------------------------------------------------------------ */
/* Class Members */
/* ------------------------------------------------------------------------ */
private:
Integ integrator;
Shape shape_functions;
};
} // namespace akantu
/* -------------------------------------------------------------------------- */
/* inline functions */
/* -------------------------------------------------------------------------- */
#include "fe_engine_template_tmpl.hh"
#include "fe_engine_template_tmpl_field.hh"
/* -------------------------------------------------------------------------- */
/* Shape Linked specialization */
/* -------------------------------------------------------------------------- */
#if defined(AKANTU_STRUCTURAL_MECHANICS)
#include "fe_engine_template_tmpl_struct.hh"
#endif
/* -------------------------------------------------------------------------- */
/* Shape IGFEM specialization */
/* -------------------------------------------------------------------------- */
#if defined(AKANTU_IGFEM)
#include "fe_engine_template_tmpl_igfem.hh"
#endif
#endif /* AKANTU_FE_ENGINE_TEMPLATE_HH_ */

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